In nine games, A wins five games with score differences of 12, 3, 8, 4 and 1, while in the remaining four games, he loses with score differences of -4, -1, -2 and -3. The average score difference of A in all the nine games is:
Average Score Difference Calculation
This solution details the process of finding the average score difference for player A across nine games, using the provided results of games won and lost.
Analyzing Game Results
Here's a breakdown of the information provided:
- Total games played: 9
- Games won: 5 with score differences of 12, 3, 8, 4, and 1.
- Games lost: 4 with score differences of -4, -1, -2, and -3.
Calculating Total Score Difference
To find the average, we first sum the score differences from all nine games.
Step 1: Sum the score differences from the games A won.
Sum of differences in won games = $12 + 3 + 8 + 4 + 1 = 28$
Step 2: Sum the score differences from the games A lost.
Sum of differences in lost games = $(-4) + (-1) + (-2) + (-3) = -10$
Step 3: Combine the sums to find the total score difference across all nine games.
Total score difference = (Sum of won game differences) + (Sum of lost game differences)
Total score difference = $28 + (-10) = 18$
Determining the Average Score Difference
The average score difference is obtained by dividing the total score difference by the total number of games played.
Average Formula:
$$ \text{Average Score Difference} = \frac{\text{Total Score Difference}}{\text{Total Number of Games}} $$
Applying the values:
Average Score Difference = $ \frac{18}{9} $
Average Score Difference = $ 2 $
Conclusion
The average score difference for player A across the nine games is 2.
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